Introduction

The dataset used is already clean thus no nead to deal with NA’s or other irregularities of similar nature.

Initial exploratory data analysis

Data1 <- as_tibble(Crime_Economics_data)

Data1$`Per Capita Income` <-  gsub(",", " ", Data1$`Per Capita Income`)
Data1$`Population Density (per sq. km)` <-  gsub(",", " ", Data1$`Population Density (per sq. km)`)
Data1$`Per Capita Income` <-  gsub(" ", "", Data1$`Per Capita Income`)
Data1$`Population Density (per sq. km)` <-  gsub(" ", "", Data1$`Population Density (per sq. km)`)
sapply(Data1[,-1], as.numeric)
##        Crime Rate Unemployment (%)  HDI Population Density (per sq. km)
##   [1,]      76.31             11.2 0.51                              57
##   [2,]      42.53             11.3 0.80                             100
##   [3,]      52.03             11.5 0.75                              18
##   [4,]      63.82              7.0 0.85                              16
##   [5,]      22.79              7.7 0.78                              99
##   [6,]      43.03              7.1 0.94                               3
##   [7,]      25.54              5.7 0.92                             106
##   [8,]      32.02              6.0 0.76                             115
##   [9,]      63.90              4.2 0.63                            1087
##  [10,]      59.58              4.6 0.82                              46
##  [11,]      44.58              5.3 0.93                             376
##  [12,]      57.77              3.5 0.72                              10
##  [13,]      42.99             18.4 0.78                              65
##  [14,]      67.49              2.9 0.77                              25
##  [15,]      38.21              4.7 0.82                              64
##  [16,]      51.13              0.7 0.59                              90
##  [17,]      65.24              3.4 0.56                              53
##  [18,]      41.89              6.9 0.93                               4
##  [19,]      53.42             10.4 0.85                              25
##  [20,]      30.14              6.7 0.76                             149
##  [21,]      56.87             14.2 0.77                              43
##  [22,]      54.22             22.0 0.81                              98
##  [23,]      24.59              7.5 0.85                              73
##  [24,]      31.28              9.4 0.89                             129
##  [25,]      25.52              9.3 0.90                             135
##  [26,]      26.22              5.7 0.94                             133
##  [27,]      61.02              5.9 0.76                             221
##  [28,]      55.23              4.9 0.76                              67
##  [29,]      46.83              5.7 0.71                              98
##  [30,]      67.79              4.2 0.67                             305
##  [31,]      23.71              6.8 0.89                              29
##  [32,]      49.30              1.5 0.49                              99
##  [33,]      27.59              8.4 0.94                              16
##  [34,]      51.99             11.9 0.90                             118
##  [35,]      23.38             20.4 0.81                              57
##  [36,]      35.79              5.4 0.95                             233
##  [37,]      46.98              1.0 0.61                             125
##  [38,]      45.85              6.8 0.89                              80
##  [39,]      58.67              1.0 0.66                             158
##  [40,]      74.54              5.2 0.63                              85
##  [41,]      22.00              6.4 0.95                            6677
##  [42,]      34.36              4.9 0.85                             104
##  [43,]      23.75              7.2 0.95                               3
##  [44,]      44.43              7.9 0.65                             411
##  [45,]      45.93              7.1 0.72                             140
##  [46,]      49.38             11.2 0.78                              50
##  [47,]      48.42             12.8 0.67                              88
##  [48,]      45.51              1.9 0.96                              69
##  [49,]      31.47              2.9 0.92                             431
##  [50,]      44.85             10.7 0.89                             201
##  [51,]      67.42              7.9 0.73                             267
##  [52,]      22.19              1.6 0.92                             337
##  [53,]      39.96             14.6 0.73                             112
##  [54,]      53.77              5.0 0.83                               7
##  [55,]      60.14              2.6 0.60                              87
##  [56,]      56.87              6.6 0.70                              32
##  [57,]      38.77              8.5 0.87                              30
##  [58,]      46.77              6.3 0.74                             656
##  [59,]      61.78             18.6 0.72                               4
##  [60,]      33.42              9.6 0.88                              43
##  [61,]      34.13              2.5 0.92                             234
##  [62,]      57.29              4.6 0.81                              95
##  [63,]      55.34              6.4 0.74                            1719
##  [64,]      40.39              3.9 0.90                            1390
##  [65,]      48.88             30.0 0.80                             644
##  [66,]      54.19              3.8 0.78                              64
##  [67,]      46.35              2.0 0.75                             120
##  [68,]      56.01              5.9 0.74                               2
##  [69,]      41.18              5.6 0.83                              45
##  [70,]      48.66             12.7 0.69                              81
##  [71,]      46.51              1.7 0.58                              79
##  [72,]      65.21             23.0 0.65                               3
##  [73,]      36.01              2.6 0.60                             191
##  [74,]      27.16             12.8 0.94                             457
##  [75,]      42.88              5.3 0.93                              18
##  [76,]      47.89              7.4 0.66                              50
##  [77,]      64.06              2.7 0.54                             212
##  [78,]      39.12             11.2 0.77                              81
##  [79,]      33.72              3.5 0.96                              16
##  [80,]      42.51              4.4 0.56                             241
##  [81,]      45.15              3.8 0.82                              55
##  [82,]      49.37              5.7 0.73                              17
##  [83,]      66.72             16.4 0.78                              25
##  [84,]      42.46             10.0 0.72                             356
##  [85,]      30.50              3.1 0.88                             122
##  [86,]      29.91              7.2 0.86                             111
##  [87,]      28.30              5.7 0.83                              82
##  [88,]      39.99              6.3 0.82                               9
##  [89,]      24.89             14.0 0.54                             467
##  [90,]      25.23              7.5 0.85                              16
##  [91,]      38.10              7.3 0.81                             100
##  [92,]      27.96              3.6 0.94                            8041
##  [93,]      30.37              7.0 0.86                             111
##  [94,]      22.28              4.9 0.92                             102
##  [95,]      76.86             35.3 0.71                              47
##  [96,]      26.68              4.2 0.92                             511
##  [97,]      33.32             13.3 0.90                              92
##  [98,]      41.39              5.4 0.78                             324
##  [99,]      48.00              8.9 0.95                              22
## [100,]      21.62              5.1 0.96                             207
## [101,]      56.00              2.0 0.53                              59
## [102,]      39.35              1.9 0.78                             135
## [103,]      43.69             16.2 0.74                              71
## [104,]      39.62             12.7 0.82                             105
## [105,]      56.12              1.9 0.54                             177
## [106,]      47.42              9.9 0.78                              73
## [107,]      15.23              2.4 0.89                             115
## [108,]      47.81              3.8 0.93                              34
## [109,]      51.73             11.1 0.82                              20
## [110,]      33.42              8.9 0.72                              73
## [111,]      83.76              9.4 0.71                              32
## [112,]      46.19              8.8 0.70                             289
## [113,]      43.62             11.4 0.58                              23
## [114,]      59.30              5.0 0.57                              37
##        Weapons per 100 persons Per Capita Income Gini Coefficient Literacy Rate
##   [1,]                    12.5               508            27.80          0.38
##   [2,]                    12.0              5181            33.20          0.98
##   [3,]                     2.1              3368            27.60          0.80
##   [4,]                     7.4              8476            41.40          0.98
##   [5,]                     6.1              4266            34.40          1.00
##   [6,]                    14.5             55823            34.40          0.99
##   [7,]                    30.0             48106            29.70          0.99
##   [8,]                     3.6              4202            26.60          1.00
##   [9,]                     0.4              2001            32.40          0.76
##  [10,]                     6.1              6377            25.20          1.00
##  [11,]                    12.7             45028            27.40          0.99
##  [12,]                     2.0              3133            42.20          0.96
##  [13,]                    31.2              6035            33.00          0.99
##  [14,]                     8.3              6797            53.30          0.92
##  [15,]                     8.4             10058            40.40          0.98
##  [16,]                     4.5              1513            69.20          0.77
##  [17,]                     2.1              1502            46.60          0.75
##  [18,]                    34.7             43560            33.80          0.99
##  [19,]                    12.1             13232            44.40          0.97
##  [20,]                     3.6             10229            38.50          0.96
##  [21,]                    10.1              5333            50.40          0.95
##  [22,]                    10.0             12077            48.00          0.79
##  [23,]                    13.7             13934            30.40          0.98
##  [24,]                    34.0             28133            31.40          1.00
##  [25,]                    12.5             22911            24.90          0.99
##  [26,]                     9.9             61477            28.70          0.99
##  [27,]                     7.4              7268            43.70          0.92
##  [28,]                     2.4              5600            45.40          0.68
##  [29,]                     4.1              3609            31.50          0.95
##  [30,]                    12.0              3799            38.60          0.75
##  [31,]                     5.0             23106            30.40          0.74
##  [32,]                     0.4               840            35.00          0.49
##  [33,]                    32.4             48685            27.40          0.99
##  [34,]                    19.6             38959            31.60          0.99
##  [35,]                    10.1              3984            36.40          1.00
##  [36,]                    19.6             45909            31.90          0.99
##  [37,]                     8.0              2206            43.50          0.77
##  [38,]                    17.6             18117            34.40          0.98
##  [39,]                    12.1              4332            48.30          0.79
##  [40,]                    14.1              2406            52.10          0.89
##  [41,]                     3.6             46611            46.70          0.99
##  [42,]                    10.5             16129            30.60          0.99
##  [43,]                    31.7             63644            26.80          0.99
##  [44,]                     5.3              1931            37.80          0.74
##  [45,]                     0.0              3870            39.00          0.94
##  [46,]                     7.3             11183            40.80          0.87
##  [47,]                    19.6              4146            29.50          0.44
##  [48,]                     7.2             86251            32.80          0.99
##  [49,]                     6.7             47034            39.00          0.97
##  [50,]                    14.4             31238            35.90          0.99
##  [51,]                     8.8              4665            45.50          0.89
##  [52,]                     0.3             39990            32.90          0.99
##  [53,]                    18.7              4283            33.70          0.98
##  [54,]                     2.8              9111            27.50          1.00
##  [55,]                     1.5              1879            40.80          0.78
##  [56,]                     2.8              1186            27.70          1.00
##  [57,]                    10.5             17871            35.60          1.00
##  [58,]                    31.9              9310            31.80          0.94
##  [59,]                    13.3              4243            69.30          0.91
##  [60,]                    13.6             20772            37.30          1.00
##  [61,]                    18.9            117182            34.90          0.99
##  [62,]                     0.7             10402            41.00          0.66
##  [63,]                     6.2              6924            31.30          0.95
##  [64,]                    28.3             33771            29.20          0.39
##  [65,]                     8.3              8587            36.80          0.91
##  [66,]                    12.9              8326            45.40          0.94
##  [67,]                     3.0              2954            25.70          0.99
##  [68,]                     7.9              4007            32.70          0.98
##  [69,]                    39.1              7626            39.00          0.99
##  [70,]                     4.8              3108            39.50          0.74
##  [71,]                     1.6              1292            30.70          0.76
##  [72,]                    15.4              4215            59.10          0.82
##  [73,]                     1.5              1135            32.80          0.65
##  [74,]                     2.6             53334            28.50          0.99
##  [75,]                    26.3             43972            32.50          0.99
##  [76,]                     5.2              1905            46.20          0.83
##  [77,]                     3.2              2085            35.10          0.60
##  [78,]                    29.8              5886            34.20          1.00
##  [79,]                    28.8             66871            27.00          0.99
##  [80,]                    22.3              1167            33.50          0.59
##  [81,]                    10.8             12269            49.20          0.95
##  [82,]                    16.7              4950            46.20          0.96
##  [83,]                     2.0              6163            42.80          0.95
##  [84,]                     3.6              3299            44.40          0.96
##  [85,]                     2.5             15764            29.70          1.00
##  [86,]                    21.3             22413            33.80          0.95
##  [87,]                     2.6             12929            36.00          0.99
##  [88,]                    12.3             10166            37.50          1.00
##  [89,]                     0.5               798            43.70          0.71
##  [90,]                    16.7             20110            54.10          0.95
##  [91,]                    39.1              7656            36.20          0.98
##  [92,]                     0.3             58114             0.36          0.97
##  [93,]                     6.5             19264            25.20          1.00
##  [94,]                    15.6             25777            24.20          1.00
##  [95,]                     9.7              5094            63.00          0.94
##  [96,]                     0.2             31947            31.60          0.98
##  [97,]                     7.5             27409            34.70          0.98
##  [98,]                     2.4              3768            39.80          0.93
##  [99,]                    23.1             53575            28.80          0.99
## [100,]                    27.6             86919            32.70          0.99
## [101,]                     0.8              1115            40.50          0.80
## [102,]                    15.1              7189            36.40          0.97
## [103,]                     1.1              3318            32.80          0.82
## [104,]                    16.5              8538            41.90          0.95
## [105,]                     0.8               846            42.80          0.74
## [106,]                     9.9              3557            26.10          1.00
## [107,]                    16.7             36285            32.50          0.94
## [108,]                   120.5             63123            34.80          0.86
## [109,]                    34.7             15438            41.40          0.98
## [110,]                     0.4              1724            39.70          1.00
## [111,]                    18.5              3740            46.90          0.95
## [112,]                     1.6              2786            35.70          0.95
## [113,]                     0.9               985            57.10          0.63
## [114,]                     2.8              1466            44.30          0.87
##        Happiness Index
##   [1,]            2.52
##   [2,]            5.12
##   [3,]            4.89
##   [4,]            5.93
##   [5,]            5.28
##   [6,]            7.18
##   [7,]            7.27
##   [8,]            5.17
##   [9,]            5.03
##  [10,]            5.53
##  [11,]            6.83
##  [12,]            5.72
##  [13,]            5.81
##  [14,]            6.33
##  [15,]            5.27
##  [16,]            4.83
##  [17,]            5.14
##  [18,]            7.10
##  [19,]            6.17
##  [20,]            5.34
##  [21,]            6.01
##  [22,]            7.07
##  [23,]            5.88
##  [24,]            6.22
##  [25,]            6.97
##  [26,]            7.62
##  [27,]            5.55
##  [28,]            5.76
##  [29,]            4.28
##  [30,]            6.06
##  [31,]            6.19
##  [32,]            4.28
##  [33,]            7.84
##  [34,]            6.69
##  [35,]            4.89
##  [36,]            7.16
##  [37,]            5.09
##  [38,]            5.72
##  [39,]            6.44
##  [40,]            5.92
##  [41,]            5.48
##  [42,]            5.99
##  [43,]            7.55
##  [44,]            3.82
##  [45,]            5.35
##  [46,]            4.72
##  [47,]            4.85
##  [48,]            7.09
##  [49,]            7.16
##  [50,]            6.48
##  [51,]            6.31
##  [52,]            5.94
##  [53,]            4.40
##  [54,]            6.15
##  [55,]            4.61
##  [56,]            5.74
##  [57,]            6.03
##  [58,]            4.58
##  [59,]            5.41
##  [60,]            6.26
##  [61,]            7.32
##  [62,]            5.38
##  [63,]            5.20
##  [64,]            6.60
##  [65,]            6.05
##  [66,]            6.32
##  [67,]            5.77
##  [68,]            5.68
##  [69,]            5.58
##  [70,]            4.92
##  [71,]            4.43
##  [72,]            4.57
##  [73,]            5.27
##  [74,]            7.46
##  [75,]            7.28
##  [76,]            5.97
##  [77,]            4.76
##  [78,]            5.10
##  [79,]            7.39
##  [80,]            4.93
##  [81,]            6.18
##  [82,]            5.65
##  [83,]            5.84
##  [84,]            5.88
##  [85,]            6.17
##  [86,]            5.93
##  [87,]            6.14
##  [88,]            5.48
##  [89,]            3.42
##  [90,]            6.49
##  [91,]            6.08
##  [92,]            6.38
##  [93,]            6.33
##  [94,]            6.46
##  [95,]            4.96
##  [96,]            5.85
##  [97,]            6.49
##  [98,]            4.33
##  [99,]            7.36
## [100,]            7.57
## [101,]            3.62
## [102,]            5.99
## [103,]            4.60
## [104,]            4.95
## [105,]            4.64
## [106,]            4.88
## [107,]            6.56
## [108,]            6.95
## [109,]            6.43
## [110,]            6.18
## [111,]            4.89
## [112,]            5.41
## [113,]            4.07
## [114,]            3.15
Data1 <- sapply(Data1[,-1], as.numeric)
Data1 <- as_tibble(Data1)



source("Code/dens_plot.R")

dens_plot(alpha = 0.7, binwidth = 4)

source("Code/dens_plot_log.R")
dens_plot_log(alpha = 0.7, binwidth = 0.2)

The density plot is nearly normally distributed with some outliers in the lower quantiles.

source("Code/predictor_Corr.R")
## corrplot 0.92 loaded

## Loading required package: plotly
## 
## Attaching package: 'plotly'
## The following object is masked from 'package:ggplot2':
## 
##     last_plot
## The following object is masked from 'package:stats':
## 
##     filter
## The following object is masked from 'package:graphics':
## 
##     layout
## Loading required package: viridis
## Loading required package: viridisLite
## 
## ======================
## Welcome to heatmaply version 1.4.2
## 
## Type citation('heatmaply') for how to cite the package.
## Type ?heatmaply for the main documentation.
## 
## The github page is: https://github.com/talgalili/heatmaply/
## Please submit your suggestions and bug-reports at: https://github.com/talgalili/heatmaply/issues
## You may ask questions at stackoverflow, use the r and heatmaply tags: 
##   https://stackoverflow.com/questions/tagged/heatmaply
## ======================
## Warning in doTryCatch(return(expr), name, parentenv, handler): unable to load shared object '/Library/Frameworks/R.framework/Resources/modules//R_X11.so':
##   dlopen(/Library/Frameworks/R.framework/Resources/modules//R_X11.so, 6): Library not loaded: /opt/X11/lib/libSM.6.dylib
##   Referenced from: /Library/Frameworks/R.framework/Versions/4.0/Resources/modules/R_X11.so
##   Reason: image not found

predictor_Corr(alpha = 0.7)

Splitting of data